Lesson 6
Welcome
Notes:
Scatterplot Review
setwd('/Users/James/Dropbox/Projects/da/eda/lesson6')
library(ggplot2)
library(ggthemes)
theme_set(theme_fivethirtyeight(12))## Warning: New theme missing the following elements: panel.margin.x,
## panel.margin.ydata(diamonds)
ggplot(diamonds, aes(carat, price)) +
xlim(0, quantile(diamonds$carat, 0.99)) +
ylim(0, quantile(diamonds$price, 0.99)) +
geom_point(fill = '#CC2127', shape = 21) +
stat_smooth(method = 'lm', color = '#007EE5') # linear trendline## Warning: Removed 926 rows containing missing values (stat_smooth).## Warning: Removed 926 rows containing missing values (geom_point).## Warning: Removed 4 rows containing missing values (geom_path).
Price and Carat Relationship
Response: Heavier diamonds seem to cost more. It looks like a non-linear, possibly exponential growth relationship. The dispersion seems to increase with higher weights. ***
Frances Gerety
Notes:
A diamonds is
The Rise of Diamonds
Notes:
ggpairs Function
Notes: The plot matrix uses the type of plot appropriate for the type of data, (qualitative/quantitative)
# install these if necessary
# install.packages('GGally')
# install.packages('scales')
# install.packages('memisc')
# install.packages('lattice')
# install.packages('MASS')
# install.packages('car')
# install.packages('reshape2')
# install.packages('dplyr')
# load the ggplot graphics package and the others
library(ggplot2)
library(GGally)
library(scales)
library(memisc)## Loading required package: lattice
## Loading required package: MASS
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## Attaching package: 'memisc'
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## The following object is masked from 'package:scales':
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## as.array, trimws# sample 10,000 diamonds from the data set
set.seed(20022012)
diamond_samp <- diamonds[sample(1:length(diamonds$price), 10000), ]
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What are some things you notice in the ggpairs output? Response:
The Demand of Diamonds
Notes:
# histogram of price
plot1 <- ggplot(diamonds, aes(price, fill = '#CC2127')) +
geom_histogram(binwidth = 100)
ggtitle('Price')## $title
## [1] "Price"
##
## attr(,"class")
## [1] "labels"# transform the price variable using log10
plot2 <- ggplot(diamonds, aes(price, fill = '#007EE5')) +
geom_histogram(binwidth = 0.01) +
scale_x_log10() +
ggtitle('Price (log10)')
library(gridExtra)
library(grid)
grid.arrange(plot1, plot2)
Connecting Demand and Price Distributions
Notes: The log plot emphasizes a more normal bimodal distribution, while the standard plot skews heavily towards the right. ***
Scatterplot Transformation
ggplot(diamonds, aes(carat, price)) +
geom_point(alpha = 1/20, color = '#007EE5') +
scale_x_continuous(trans = log10_trans()) +
ggtitle('Price (log10) by Carat')
Create a new function to transform the carat variable
cuberoot_trans = function() trans_new('cuberoot',
transform = function(x) x^(1/3),
inverse = function(x) x^3)Use the cuberoot_trans function
ggplot(aes(carat, price), data = diamonds) +
geom_point() +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat')## Warning: Removed 1683 rows containing missing values (geom_point).
Overplotting Revisited
head(sort(table(diamonds$carat), decreasing = T))##
## 0.3 0.31 1.01 0.7 0.32 1
## 2604 2249 2242 1981 1840 1558head(sort(table(diamonds$price), decreasing = T))##
## 605 802 625 828 776 698
## 132 127 126 125 124 121ggplot(aes(carat, price), data = diamonds) +
geom_point(alpha = 1/2, size = 3/4, position = 'jitter') +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat')## Warning: Removed 1691 rows containing missing values (geom_point).
Other Qualitative Factors
Notes:
Price vs. Carat and Clarity
Alter the code below.
# install and load the RColorBrewer package
# install.packages('RColorBrewer')
library(RColorBrewer)
ggplot(aes(x = carat, y = price, color = clarity), data = diamonds) +
geom_point(alpha = 0.5, size = 1, position = 'jitter') +
scale_color_brewer(type = 'div',
guide = guide_legend(title = 'Clarity', reverse = T,
override.aes = list(alpha = 1, size = 2))) +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat and Clarity')## Warning: Removed 1693 rows containing missing values (geom_point).
Clarity and Price
Response: Yes, controlling for carat, clearer diamonds exhibit higher prices. ***
Price vs. Carat and Cut
Alter the code below.
ggplot(aes(x = carat, y = price, color = cut), data = diamonds) +
geom_point(alpha = 0.5, size = 1, position = 'jitter') +
scale_color_brewer(type = 'div',
guide = guide_legend(title = 'Cut', reverse = T,
override.aes = list(alpha = 1, size = 2))) +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat and Cut')## Warning: Removed 1696 rows containing missing values (geom_point).
Cut and Price
Response: Somewhat. Better cuts exhibit more variance in price, but most diamonds are close to ideal anyways. ***
Price vs. Carat and Color
Alter the code below.
ggplot(aes(x = carat, y = price, color = color), data = diamonds) +
geom_point(alpha = 0.5, size = 1, position = 'jitter') +
scale_color_brewer(type = 'div',
guide = guide_legend(title = 'Color',
override.aes = list(alpha = 1, size = 2))) +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat and Color')## Warning: Removed 1688 rows containing missing values (geom_point).
Color and Price
Response: Most definitely, controlling for carat, better colors exhibit higher prices. ***
Linear Models in R
Notes: lm(y ~ x), where y = outcome variable, x = explanatory variable
Response: lm( log(price) ~ carat^(1/3) ) ***
Building the Linear Model
Notes:
m1 <- lm(I(log(price)) ~ I(carat^(1/3)), data = diamonds)
m2 <- update(m1, ~ . + carat)
m3 <- update(m2, ~ . + cut)
m4 <- update(m3, ~ . + color)
m5 <- update(m4, ~ . + clarity)
mtable(m1, m2, m3, m4, m5)##
## Calls:
## m1: lm(formula = I(log(price)) ~ I(carat^(1/3)), data = diamonds)
## m2: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat, data = diamonds)
## m3: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut, data = diamonds)
## m4: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color,
## data = diamonds)
## m5: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color +
## clarity, data = diamonds)
##
## ======================================================================
## m1 m2 m3 m4 m5
## ----------------------------------------------------------------------
## (Intercept) 2.821*** 1.039*** 0.874*** 0.932*** 0.415***
## (0.006) (0.019) (0.019) (0.017) (0.010)
## I(carat^(1/3)) 5.558*** 8.568*** 8.703*** 8.438*** 9.144***
## (0.007) (0.032) (0.031) (0.028) (0.016)
## carat -1.137*** -1.163*** -0.992*** -1.093***
## (0.012) (0.011) (0.010) (0.006)
## cut: .L 0.224*** 0.224*** 0.120***
## (0.004) (0.004) (0.002)
## cut: .Q -0.062*** -0.062*** -0.031***
## (0.004) (0.003) (0.002)
## cut: .C 0.051*** 0.052*** 0.014***
## (0.003) (0.003) (0.002)
## cut: ^4 0.018*** 0.018*** -0.002
## (0.003) (0.002) (0.001)
## color: .L -0.373*** -0.441***
## (0.003) (0.002)
## color: .Q -0.129*** -0.093***
## (0.003) (0.002)
## color: .C 0.001 -0.013***
## (0.003) (0.002)
## color: ^4 0.029*** 0.012***
## (0.003) (0.002)
## color: ^5 -0.016*** -0.003*
## (0.003) (0.001)
## color: ^6 -0.023*** 0.001
## (0.002) (0.001)
## clarity: .L 0.907***
## (0.003)
## clarity: .Q -0.240***
## (0.003)
## clarity: .C 0.131***
## (0.003)
## clarity: ^4 -0.063***
## (0.002)
## clarity: ^5 0.026***
## (0.002)
## clarity: ^6 -0.002
## (0.002)
## clarity: ^7 0.032***
## (0.001)
## ----------------------------------------------------------------------
## R-squared 0.924 0.935 0.939 0.951 0.984
## adj. R-squared 0.924 0.935 0.939 0.951 0.984
## sigma 0.280 0.259 0.250 0.224 0.129
## F 652012.063 387489.366 138654.523 87959.467 173791.084
## p 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -7962.499 -3631.319 -1837.416 4235.240 34091.272
## Deviance 4242.831 3613.360 3380.837 2699.212 892.214
## AIC 15930.999 7270.637 3690.832 -8442.481 -68140.544
## BIC 15957.685 7306.220 3761.997 -8317.942 -67953.736
## N 53940 53940 53940 53940 53940
## ======================================================================Notice how adding cut to our model does not help explain much of the variance in the price of diamonds. This fits with out exploration earlier.
Model Problems
Video Notes:
Research: (Take some time to come up with 2-4 problems for the model) (You should 10-20 min on this)
Response: The timing that the prices were collecte werent held constant, so it may be subject to inflation and market changes ***
A Bigger, Better Data Set
Notes:
#install.packages('bitops')
#install.packages('RCurl')
#library('bitops')
#library('RCurl')
#diamondsurl = getBinaryURL("https://raw.github.com/solomonm/diamonds-data/master/BigDiamonds.Rda")
#load(rawConnection(diamondsurl))
load("BigDiamonds.rda")The code used to obtain the data is available here: https://github.com/solomonm/diamonds-data
Building a Model Using the Big Diamonds Data Set
Notes:
# sampling the big diamonds dataset
diamondbig_samp <- diamondsbig[sample(1:length(diamondsbig$price), 10000), ]
# 5 models
m1 <- lm(I(log(price)) ~ I(carat^(1/3)),
data = subset(diamondbig_samp, price < 10000 & cert == 'GIA'))
m2 <- update(m1, ~ . + carat)
m3 <- update(m2, ~ . + cut)
m4 <- update(m3, ~ . + color)
m5 <- update(m4, ~ . + clarity)
mtable(m1, m2, m3, m4, m5)##
## Calls:
## m1: lm(formula = I(log(price)) ~ I(carat^(1/3)), data = subset(diamondbig_samp,
## price < 10000 & cert == "GIA"))
## m2: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat, data = subset(diamondbig_samp,
## price < 10000 & cert == "GIA"))
## m3: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut, data = subset(diamondbig_samp,
## price < 10000 & cert == "GIA"))
## m4: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color,
## data = subset(diamondbig_samp, price < 10000 & cert == "GIA"))
## m5: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color +
## clarity, data = subset(diamondbig_samp, price < 10000 & cert ==
## "GIA"))
##
## =================================================================
## m1 m2 m3 m4 m5
## -----------------------------------------------------------------
## (Intercept) 2.687*** 1.184*** 0.786*** 0.348*** -0.628***
## (0.024) (0.094) (0.093) (0.077) (0.070)
## I(carat^(1/3)) 5.819*** 8.514*** 8.935*** 8.348*** 8.557***
## (0.028) (0.165) (0.162) (0.130) (0.091)
## carat -1.183*** -1.363*** -0.884*** -0.858***
## (0.072) (0.070) (0.057) (0.040)
## cut: V.Good 0.113*** 0.099*** 0.078***
## (0.013) (0.010) (0.007)
## cut: Ideal 0.213*** 0.196*** 0.140***
## (0.012) (0.009) (0.007)
## color: K/L 0.148*** 0.117***
## (0.028) (0.020)
## color: J/L 0.345*** 0.323***
## (0.026) (0.018)
## color: I/L 0.493*** 0.474***
## (0.026) (0.018)
## color: H/L 0.594*** 0.611***
## (0.026) (0.018)
## color: G/L 0.662*** 0.669***
## (0.025) (0.018)
## color: F/L 0.720*** 0.732***
## (0.025) (0.018)
## color: E/L 0.759*** 0.762***
## (0.025) (0.018)
## color: D/L 0.855*** 0.835***
## (0.026) (0.018)
## clarity: I1 0.320***
## (0.048)
## clarity: SI2 0.615***
## (0.047)
## clarity: SI1 0.744***
## (0.047)
## clarity: VS2 0.850***
## (0.047)
## clarity: VS1 0.900***
## (0.047)
## clarity: VVS2 0.945***
## (0.047)
## clarity: VVS1 1.016***
## (0.047)
## clarity: IF 1.085***
## (0.048)
## -----------------------------------------------------------------
## R-squared 0.886 0.891 0.898 0.936 0.969
## adj. R-squared 0.886 0.891 0.898 0.936 0.969
## sigma 0.294 0.287 0.278 0.220 0.154
## F 44130.817 23257.268 12518.614 6914.312 8736.670
## p 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -1096.903 -963.798 -775.655 544.199 2564.522
## Deviance 489.078 466.666 436.727 274.283 134.579
## AIC 2199.806 1935.597 1563.310 -1060.398 -5085.043
## BIC 2219.738 1962.172 1603.173 -967.384 -4938.879
## N 5675 5675 5675 5675 5675
## =================================================================Predictions
Example Diamond from BlueNile: Round 1.00 Very Good I VS1 $5,601
#Be sure you’ve loaded the library memisc and have m5 saved as an object in your workspace.
thisDiamond = data.frame(carat = 1.00, cut = "V.Good",
color = "I", clarity="VS1")
modelEstimate = predict(m5, newdata = thisDiamond,
interval="prediction", level = .95)
exp(modelEstimate)## fit lwr upr
## 1 5024.202 3711.116 6801.891Evaluate how well the model predicts the BlueNile diamond’s price. Think about the fitted point estimate as well as the 95% CI.
The fitted point estimate of $5046.85 is quite close to the actual price $5601.
The 95% CI of (3719.35, 6848.16) is quite generous, and the actual price is within these bounds. ***
Final Thoughts
Notes:
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